Boyce preferred to be called by a shorten version of his middle name, Larry. He was born in Kannapolis, North Carolina, the son of Margaret Authelee Moore and Boyce Lowrance Duncan Sr. He had an older sister, Betty and a younger brother. Boyce grew up in Las Cruces and Alamogardo, New Mexico and had lived in Odessa for a short period of time. Larry's father had served in World War II, as a member of the 456th Bomb Group, as a flight engineer. Larry joined the Army in Odessa July 14, 1964 on a four year enlistment and was inducted in Abilene, Texas.

He began his tour in Vietnam on January 9, 1966. He served a year and then extended his tour for three six months extensions. He had planned on getting out of the military when his current extension was completed. He was assigned to Advisory Team 51, MACV Advisors, Military Assistance Command-Vietnam during his last extension. On January 23, 1968, he was in altercation with an individual and he was shot in the right upper chest. The weapon used was a Carbine rifle.

Specialist Duncan was buried with full military honors at the Fort Bliss National Cemetery in El Paso, Texas. His parents were living in Alamogardo, New Mexico at the time of his death.